\newproblem{lay:2_9_3}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 2.9.3}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
  $\mathbf{x}=\begin{pmatrix}0\\7\end{pmatrix}$ is in a subspace $H$ whose basis is $B=\left\{\mathbf{b}_1,\mathbf{b}_2\right\}$ with
	$\mathbf{b}_1=\begin{pmatrix}2\\-3\end{pmatrix}$ and $\mathbf{b}_2=\begin{pmatrix}-1\\5\end{pmatrix}$. Find the coordinates of $\mathbf{x}$ in the basis $B$.
}{
  % Solution
	Let us look for the coordinates that satisfy
	\begin{center}
		$\mathbf{x}=c_1\mathbf{b}_1+c_2\mathbf{b}_2$
	\end{center}
	For this, we will use the augmented matrix
	\begin{center}
		$\left(\begin{array}{rr|r} 2 & -1 & 0 \\ -3 & 5 & 7\end{array}\right) \sim
		 \left(\begin{array}{rr|r} 1 & 0 & 1 \\ 0 &  1 & 2\end{array}\right)$
	\end{center}
	So, the coordinates of $\mathbf{x}$ in the basis $B$ are $[\mathbf{x}]_B=\begin{pmatrix}1\\2\end{pmatrix}$.
}
\useproblem{lay:2_9_3}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
